Non-Planar Voltage Multiplier

ABSTRACT

In order to reduce the amount of electrical insulation needed for voltage isolation of large voltages generated by a voltage multiplier, the voltage multiplier can be shaped to smooth out electric field gradients. The voltage multiplier can comprise multiple sections, each section located in a different plane. The voltage multiplier can comprise a negative voltage multiplier and a positive voltage multiplier, each inclined at different angles with respect to each other. The voltage multiplier can include a curved shape.

CLAIM OF PRIORITY

This is a continuation of U.S. patent application Ser. No. 16/142,334,filed on Sep. 26, 2018, which claims priority to claims priority to U.S.Provisional Patent Application No. 62/587,147, filed on Nov. 16, 2017,which are incorporated herein by reference.

FIELD OF THE INVENTION

The present application is related generally to x-ray sources.

BACKGROUND

Voltage multipliers can generate many kilovolts of voltage differential.In an x-ray source, this voltage differential can be used to causeelectrons to emit from a cathode, impede onto an anode, and generatex-rays. Electrical insulation for isolating this voltage differentialcan be heavy and expensive. The weight of such electrical insulation canbe particularly problematic for portable devices (e.g. portable x-raysources). The size of the electrical insulation can be a problem if thedevice needs to be inserted into a small location. It would be desirableto reduce the amount of electrical insulation needed for voltageisolation of large voltages generated by voltage multipliers.

SUMMARY

It has been recognized that it would be advantageous to reduce theamount of electrical insulation needed for voltage isolation of largevoltages generated by voltage multipliers. The present invention isdirected to various embodiments of voltage multipliers that satisfy thisneed. The voltage multiplier can be shaped to smooth out electric fieldgradients, resulting in less required electrical insulation.

In one embodiment, the voltage multiplier can comprise a low voltagesection located in a first plane and a high voltage section located in asecond plane. The first plane and the second plane can form a V-shape.

In another embodiment, the voltage multiplier can comprise a negativevoltage multiplier and a positive voltage multiplier. The negativevoltage multiplier and the positive voltage multiplier can be inclinedat different angles with respect to each other such that a side view ofthe voltage multipliers forms an X-shape by intersection of planes ofthe voltage multipliers.

In another embodiment, the voltage multiplier can comprise a first endhaving a lowest absolute value of voltage and a second end having ahighest absolute value of voltage, and a gradually increasing absolutevalue of voltage from the first end to the second end. The voltagemultiplier can also include a curved shape with a direction of theincreasing absolute value of voltage wrapping in the curved shape atleast partially around a voltage multiplier axis.

BRIEF DESCRIPTION OF THE DRAWINGS (DRAWINGS MIGHT NOT BE DRAWN TO SCALE)

FIG. 1 is a schematic, end-view of a voltage multiplier 10 comprising alow voltage section 11 located in a first plane P₁ and a high voltagesection 12 located in a second plane P₂, the first plane P₁ and thesecond plane P₂ forming a V-shape with an angle A₁ of a channel of theV-shape, in accordance with an embodiment of the present invention.

FIG. 2 is a schematic perspective-view of voltage multiplier 10 of FIG.1, in accordance with an embodiment of the present invention.

FIG. 3a is a schematic, end-view of an x-ray source 30 a comprisingvoltage multiplier 10 of FIG. 1, the x-ray source 30 a furthercomprising: (i) an x-ray tube 30 in a channel 19 of the V-shape with anx-ray tube axis 31 aligned with the channel 19 of the V-shape; and (ii)a corona guard 35 with a curved profile wrapping at least partiallyaround the voltage multiplier 10 and the x-ray tube 30; in accordancewith an embodiment of the present invention.

FIG. 3b is a schematic, end-view of an x-ray source 30 b, similar tox-ray source 30 a, but further comprising a voltage sensor 39 on aconvex side of the curved profile of the corona guard 35, in accordancewith an embodiment of the present invention.

FIGS. 4 & 5 are schematic perspective-views of x-ray sources 40 & 50,similar to x-ray sources 30 a & 30 b, but without the corona guard 35and the voltage sensor 39, in accordance with embodiments of the presentinvention.

FIG. 6 is a schematic, end-view of a voltage multiplier 60, similar tovoltage multiplier 10, but further comprising a middle voltage section61 electrically coupled between the low voltage section 11 and the highvoltage section 12, in accordance with an embodiment of the presentinvention.

FIGS. 7a-b are schematic, end-views of x-ray sources 70 a and 70 b,similar to the x-ray sources in FIGS. 3a -5, but the V-shape is aprimary V-shape, the voltage multiplier 10 is a negative voltagemultiplier 76, the low voltage section 11 is a negative low voltagesection 71, and the high voltage section 12 is a negative high voltagesection 72; the x-ray source further comprising a positive voltagemultiplier 86 including a positive low voltage section 81 located in athird plane P₃ and a positive high voltage section 82 located in afourth plane P₄, the third plane P₃ and the fourth plane P₄ forming asecondary V-shape with an angle A₂ of an channel 89 of the secondaryV-shape; in accordance with embodiments of the present invention.

FIG. 8 is a schematic, end-view of an x-ray source 80, similar to x-raysource 70, but further comprising a first vector V₁, a second vector V₂,and an angle A₅ between the first vector V₁ and the second vector V₂, inaccordance with an embodiment of the present invention.

FIG. 9 is a schematic, top-view of x-ray source 80, in accordance withan embodiment of the present invention.

FIGS. 10a-b are schematic, end-view of x-ray sources 100 a and 100 b,similar to x-ray source 80, but further comprising: (i) an angle A₆between the second plane P₂ and the fourth plane P₄; (ii) a negativevoltage-sensing resistor 107 in a fifth plane P₅ and a positivevoltage-sensing resistor 108 in a sixth plane P₆; and (iii) the firstplane P₁, the second plane P₂, the third plane P₃, the fourth plane P₄,the fifth plane P₅, and the sixth plane P₆ encircling the x-ray tube 30;in accordance with embodiments of the present invention.

FIG. 11 is a schematic, end-view of x-ray source 110 comprising an x-raytube 30 arid a voltage multiplier 116, the voltage multiplier comprisinga negative voltage multiplier 111 and a positive voltage multiplier 112,the negative voltage multiplier 111 and the positive voltage multiplier112 inclined at different angles with respect to each other such that anend view of the voltage multipliers forms an X-shape by intersection ofa plane P_(N) of the negative voltage multiplier 111 and a plane P_(P)of the positive voltage multiplier 112, in accordance with an embodimentof the present invention.

FIG. 12 is a schematic, top-view of x-ray source 110, in accordance withan embodiment of the present invention.

FIG. 13 is a schematic, end-view of an x-ray source 130, similar tox-ray source 110, but further comprising a distance D_(H) between apositive high voltage end 112 _(H) and a negative high voltage end 111_(H) that is larger than a distance D_(L) between a positive low voltageend 112 _(L) and a negative low voltage end 111 _(L), in accordance withan embodiment of the present invention.

FIG. 14 is a schematic, end-view of an x-ray source 140, similar tox-ray source 110, but further comprising the voltage multipliers 111 and112 intersecting in the end view, in accordance with an embodiment ofthe present invention.

FIG. 15a is a schematic, end-view of an x-ray source 150, similar tox-ray sources 110, 130, and 140, but further comprising: (i) a coronaguard 35 with a curved profile wrapping at least partially around thevoltage multiplier 116 and the x-ray tube 30; and (ii) a negativevoltage sensor 159 electrically coupled to a negative output biasvoltage 74 and located on a convex side of the curved profile; inaccordance with an embodiment of the present invention.

FIG. 15b is a schematic, end-view of x-ray source 150, viewed from anopposite end than shown in FIG. 15a , also showing a positive voltagesensor 169 electrically coupled to a positive output bias voltage 84 andlocated on the convex side of the curved profile, in accordance with anembodiment of the present invention.

FIG. 16 is a schematic, top-view of x-ray source 150, in accordance withan embodiment of the present invention.

FIG. 17a is a schematic, end-view of a voltage multiplier 171 comprisinga first end 171 _(L) having a lowest absolute value of voltage and asecond end 171 _(H) having a highest absolute value of voltage, agradually increasing absolute value of voltage from the first end 171_(L) to the second end 171 _(H), a direction 171 _(C) of the increasingabsolute value of voltage wrapping in the curved shape at leastpartially around an axis, defining a voltage multiplier axis 173, inaccordance with an embodiment of the present invention.

FIG. 17b is a schematic, end-view of a voltage multiplier 172, similar ovoltage multiplier 171, except that whereas the curved shape of voltagemultiplier 171 is continuous and smooth, the curved shape of voltagemultiplier 172 is segmentedformed by multiple sections 174, inaccordance with an embodiment of the present invention.

FIG. 18 is a schematic, end-view of a voltage multiplier 180, similar tovoltage multipliers 171 or 172, voltage multiplier 180 including anegative voltage multiplier 181 with a primary curved shape having adirection 181 _(C) of increasing absolute value of voltage and apositive voltage multiplier 182 with a secondary curved shape having adirection 182 _(C) of increasing voltage, in accordance with anembodiment of the present invention.

FIG. 19 is a schematic, end-view of an x-ray source 190 comprising anx-ray tube 30 and voltage multiplier 180, in accordance with anembodiment of the present invention.

FIG. 20 is a schematic, top-view of x-ray source 190, in accordance it ,an embodiment of the present invention.

FIG. 21 is a schematic, end-view of an x-ray source 210, similar tox-ray source 190, but further comprising a corona guard 35 with a curvedprofile wrapping at least partially around the voltage multiplier 180and the x-ray tube 30, in accordance with an embodiment of the presentinvention.

FIG. 22 is a schematic, end-view of an x-ray source 220, similar tox-ray source 210, but further comprising a negative voltage sensor 206electrically coupled to the negative output bias voltage 74 and apositive voltage sensor 207 electrically coupled to the positive outputbias voltage 84, both located on the convex side of the curved profile,in accordance with an embodiment of the present invention.

DEFINITIONS

As used herein, the term “aligned” includes exactly aligned, such thatthe items aligned are parallel, and also includes substantially aligned,such that the items aligned extend in roughly the same direction and arenearly parallel, such as for example within 10°, within 20°, or within30° of parallel.

As used herein, the term “curved shape,” with regard to a shape of thevoltage multiplier, includes a continuous, smooth, curved shape (e.g,flexible circuit board, see FIG. 17a ) and also includes a curved shapeformed by multiple small sections hinged to form the curved shape (e.g.see sections 174 in FIG. 17b ).

As used herein, the term “kV” means kilovolt(s).

As used herein, the terms “low voltage” and “high voltage” refer to anabsolute value of the voltage, unless specified otherwise. Thus, both 20kV and −20 kV would be “high voltage” relative to 2 kV and −2 kV.

As used herein, the term “V-shape” includes a shape with two linestapering to a point or two planes tapering to a channel, and includesshapes with a larger internal angle than in a traditional V. Thus,although a traditional V has an internal angle of about 40°, the term“V-shape” as used herein includes similar shapes wherein the anglebetween the two lines or planes is ≥10° and ≤170°.

DETAILED DESCRIPTION V-Shape

As illustrated in FIGS. 1-6, voltage multipliers are shown comprising alow voltage section 11 in a first plane P₁ and a high voltage section 12in a second plane P₂. The first plane P₁ and the second plane P₂ canform a V-shape with an angle A₁ of a channel 19 of the V-shape. Examplesof angle A₁ include a, ≥10°, ≥25°, ≥45°, ≥60°, ≥70°, ≥80°, or ≥90°, and≤100°, ≤120°, ≤140°, ≤160°, ≤170°.

The low voltage section 11 can include a low voltage end 11 _(L), with alowest absolute value of voltage in the low voltage section 11, and ahigh voltage end 11 _(H), with a highest absolute value of voltage inthe low voltage section 11. The low voltage section 11 can generate avoltage differential between the low voltage end 11 _(L) and the highvoltage end 11 _(H), such as for example a voltage differential of ≥500volts, ≥1 kV, ≥10 kV, or ≥30 kV.

The high voltage section 12 can include a low voltage end 12 _(L), witha lowest absolute value of voltage in the high voltage section 12, and ahigh voltage end 12 _(H), with a highest absolute value of voltage inthe high voltage section 12. The high voltage section 12 can generate avoltage differential between the low voltage end 12 _(L) and the highvoltage end 12 _(H), such as for example a voltage differential of ≥500volts, ≥1 kV, ≥10 kV, or ≥30 kV.

The high voltage end 11 _(H) of the low voltage section 11 can provideinput electrical power to the low voltage end 12 _(L) of the highvoltage section 12 (e.g. via electrical connection 15). The high voltagesection 12 can provide output electrical power to a high voltageapparatus at an output bias voltage (represented by reference number34). Examples of the output bias voltage 34 include an absolute value of≥1 kV, ≥2 kV, ≥20 kV, or ≥60 kV.

As shown in FIGS. 3a -5, x-ray sources 30 a, 30 b, 40, and 50 cancomprise voltage multiplier 10 plus an x-ray tube 30. The x-ray tube 30can include two ends 42, one of which can be a cathode and the other ananode. The voltage multiplier 10 can be electrically coupled from thehigh voltage end 12 _(H) of the high voltage section 12 to the x-raytube 30, and can provide the output bias voltage 34 to one of the ends42 of the x-ray tube 30. The voltage multiplier 10 can also beelectrically coupled 36 from the low voltage end 11 _(L) of the lowvoltage section 11 to the x-ray tube 30. This electrically coupling 36can also be a connection to ground voltage 16 if the x-ray tube 30 ismonopolar. References to a ground voltage 16 herein can be directconnections, or through other intermediate components, to the groundvoltage 16.

The x-ray tube 30 can be located in the channel 19 of the V-shape of thevoltage multiplier 10. An x-ray tube axis 31, extending from an electronemitter associated with the cathode to a target material associated withthe anode, can be aligned with the channel 19 of the V-shape, as shownin FIGS. 3a -5.

The V-shape of the voltage multiplier 10, and alignment of the x-raytube axis 31 with the channel 19 of the V-shape, can smooth electricalfield gradients, thus allowing greater voltage standoff with reducedelectrical insulation. Consequently, the x-ray source can be smaller andlighter for a given x-ray tube voltage rating.

As shown in FIGS. 3a and 3b , the x-ray sources 30 a and 30 b canfurther comprise a corona guard 35. The corona guard 35 can include acurved profile. The curved profile can wrap at least partially aroundthe voltage multiplier 10 and/or a curved, cylindrical shape of thex-ray tube 30. Thus for example, the curved profile can wrap ≥135°,≥180°, ≥270°, or ≥315° of a 360° circumference around the voltagemultipiier 10 and/or a curved, cylindrical shape of the x-ray tube 30.For example, the curved profile of FIG. 3a wraps about 240° of the 360°circumference. The curved profile of the corona guard 35 is shown inFIGS. 3a-b with a consistent cross-sectional shape along x-ray tube axis31. The curved profile, however, can have a narrowing profile or shape(similar to a conical shape) for space saving and improved electricalfield gradients. For example, the curved profile of the corona guard 35can be closer to the x-ray tube 30 or the voltage multiplier 10 nearlower voltages and farther away near higher voltages.

The corona guard 35 can have a material at a concave side of the curvedprofile with an electrical resistivity of ≥10⁵ Ω*m, ≥10⁷ Ω*m, ≥10⁹ Ω*m,or ≥10¹¹ Ω*m. This material can be or can include ceramic. A material ata convex side of the curved profile can have a lower electricalresistivity than the material at the concave side. This provides anelectrically-insulative surface facing the voltage multiplier to reducethe chance of arcing and a surface with higher electrical conductivityat the convex side for shaping and smoothing electrical field gradients.Thus, for example, an electrical resistivity of the material at theconcave side of the curved profile divided by an electrical resistivityof the material at the convex side of the curved profile can be ≥10⁴,≥10⁶, ≥10⁸, ≥10¹⁰, ≥10¹², or ≥10 ¹⁴.

As shown in FIG. 3b , one option for the material at the convex side isa voltage sensor 39. This provides the dual benefit of providing amaterial with a lower electrical resistivity than the material at theconcave side and saves space. Voltage-sensing resistors take valuablespace, especially in portable x-ray sources, and saving this space canbe a substantial benefit. Another problem with standard voltage-sensingresistors is that they typically have a rectangular shape, with cornerswhere electrical field gradients can be high, thus increasing the chanceof arcing failure. Putting such voltage-sensing resistors 39 on thesmooth curved profile can help avoid such arcing failure. Thevoltage-sensing resistor 39 can be a dielectric ink painted on theconvex side. Other possibilities for the voltage-sensing resistor 39include wire that can be attached to the convex side or a trace of ametal (e.g. Ag, Au, Cu) attached to the convex side.

The voltage-sensing resistor 39 can wrap around a substantial portion ofthe voltage multiplier 10 and/or a curved, cylindrical shape of thex-ray tube 30, such as for example ≥135°, ≥180°, ≥270°, or ≥315° of a360° circumference of the voltage multiplier 10 and/or a curved,cylindrical shape of the x-ray tube 30. For example, the curved profileof the voltage-sensing resistor 39 of FIG. 3b wraps about 240° of a 360°circumference around the voltage multiplier 10 and the curved,cylindrical shape of the x-ray tube 30.

As shown in FIG. 5, to further smooth electrical field gradients and toreduce the chance of arcing failure, the x-ray tube 30 can be shiftedtowards the high voltage end 12 _(H) of the high voltage section 12.Thus, a location on the low voltage section 11 having a lowest absolutevalue of voltage (e.g. low voltage end 11 _(L)) can be ≥1.5 timesfarther, ≥2 times farther, ≥3 times farther, or ≥4 times farther fromthe x-ray tube 30 than a location on the high voltage section 12 havinga highest absolute value of voltage (e.g. high voltage end 12 _(H)). Inother words, D₁/D₂≥1.5, D₁/D₂≥2, D₁/D₂≥3, or D₁/D₂≥4, where D₁ is adistance between the low voltage end 11 _(L) of the low voltage section11 and the x-ray tube 30, and D₂ is a distance between the high voltageend 12 _(H) of the high voltage section 12 and the x-ray tube 30. In oneembodiment, the high voltage end 12 _(H) of the high voltage section 12can directly contact: the x-ray tube 30. The term “directly contact” ofthe prior sentence means that the electronic component(s) of the highvoltage end 12 _(H) touch the x-ray tube 30, not merely that a wireelectrically connects the high voltage end 12 _(H) to the x-ray tube 30.Thus, D₁/D₂ can equal infinity if D₂=0.

As shown in FIG. 6, voltage multiplier 60 can be similar to voltagemultiplier 10 with a first plane P₁ of a low voltage section 11 and asecond plane P₂ of a high voitage section 12 forming a V-shape, butfurther comprising a middle voltage section 61 electrically coupledbetween the low voltage section 11 and the high voltage section 12. Themiddle voltage section 61 can receive input electrical power from thehigh voltage end 11 _(H) of the low voltage section 11, can produce ≥500volts, ≥1 kV, or ≥10 kV of absolute value of bias voltage, and canprovide input electrical power to the low voltage end 12 _(L) of thehigh voltage section 12. Thus for example, the high voltage end 11 _(H)of the low voltage section 11 and the low voltage end 12 _(L) of thehigh voltage section 12 can have the same voltage, or have a voltagedifferential of ≤0.1 volt, ≤1 volt, ≤10 volts, or ≤100 volt, as shown inFIGS. 1-5, or the high voltage end 11 _(H) of the low voltage section 11and the low voltage end 12 _(L) of the high voltage section 12 can havea voltage differential of ≥500 volts, ≥1 kV, or ≥10 kV, as shown in FIG.6.

The middle voltage section 61 can be located in a seventh plane P₇. Theseventh plane P₇ can be different from the first plane P, and the secondplane P₂. An angle A₃ between the seventh plane P₇ and the first planeP₁ and an angle A₄ between the seventh plane P₇ and the second plane P₂,both located on a same side of the seventh plane P₇, can each have thesame value or different values, and such values can be of ≥5°, ≥15°,≥30°, ≥60°, or ≥90° and ≤110°, ≤130°, ≤150°, ≤170°, or ≤175°.

X-ray sources 70, 80, and 100 in FIGS. 7a -10 can comprise an x-ray tube30 and voltage multiplier 77. Voltage multiplier 77 can include anegative voltage multiplier 76 and a positive voltage multiplier 86,each of which can have characteristics of voltage multipliers 10 and 60described above.

The negative voltage multiplier 76 can include a negative low voltagesection 71 in a first plane P₁ and a negative high voltage section 72 ina second plane P₂. The first plane P₁ and the second plane P₂ can form aprimary V-shape with an angle A₁ of a channel 79 of the primary V-shape,with values of angle A₁ as described above.

The negative low voltage section 71 can include a negative low voltageend 71 _(L), with a lowest absolute value of voltage in the negative lowvoltage section 71, and a negative high voltage end 71 _(H), with ahighest absolute value of voltage in the negative low voltage section71. The negative low voltage section 71 can generate a voltagedifferential between the negative low voltage end 711 _(L) and theneoative high voltage end 71 _(H), such as for example a voltagedifferential of ≥500 volts, ≥1 kV, ≥10 kV, or ≥30 kV.

The negative high voltage section 72 can include a negative low voltageend 72 _(L), with a lowest absolute value of voltage in the negativehigh voltage section 72, and a negative high voltage end 72 _(H), with ahighest absolute value of voltage in the negative high voltage section72. The negative high voltage section 72 can generate a voltagedifferential between the negative low voltage end 72 _(L) and thenegative high voltage end 72 _(H), such as for example a voltagedifferential of a ≥500 volts, ≥1 kV, ≥10 kV, or ≥30 kV.

The negative high voltage end 71 _(H) of the negative low voltagesection 11 can provide input electrical power to the negative lowvoltage end 72 _(L) of the negative high voltage section 72. Thenegative high voltage section 72 can be electrically coupled to and canprovide output electrical power to a cathode 91 of the x-ray tube 30 ata negative output bias voltage (represented by reference number 74).Examples of the negative output bias voltage 74 include ≤−1 kV, ≤−2 kV,≤−20 kV, or ≤−60 kV.

The positive voltage multiplier 86 can include a positive low voltagesection 81 in a third plane P₃ and a positive high voltage section 12 ina fourth plane P₄. The third plane P₃ and the fourth plane P₄ can form asecondary V-shape with an angle A₂ of a channel 89 of the secondaryV-shape. Examples of angle A₂ include a ≥10°, ≥25°, ≥45°, ≥60°, ≥70°,≥80°, or ≥90°, and ≤100°, ≤120°, ≤140°, ≤160°, ≤170°.

The positive low voltage section 81 can include a positive low voltageend 81 _(L), with a lowest voltage in the positive low voltage section81, and a positive high voltage end 81 _(H), with a highest voltage inthe positive low voltage section 81. The positive low voltage section 81can generate a voltage differential between the positive low voltage end81 _(L) and the positive high voltage end 81 _(H), such as for example avoltage differential of ≥500 volts, ≥1 kV, ≥10 kV, or ≥30 kV.

The positive high voltage section 82 can include a positive low voltageend 82 _(L), with a lowest voltage in the positive high voltage section82, and a positive high voltage end 82 _(H), with a highest voltage inthe positive high voltage section 82. The positive high voltage section82 can generate a voltage differential between the positive low voltageend 82 _(L) and the positive high voltage end 82 _(H), such as forexample a voltage differential of ≥500 volts, ≥1 kV, ≥10 kV, or ≥30 kV.

The positive high voltage end 81 _(H) of the positive low voltagesection 81 can provide input electrical power to the positive lowvoltage end 82 _(L) of the positive high voltage section 82. Thepositive high voltage section 82 can be electrically coupled to and canprovide output electrical power to an anode 92 of the x-ray tube 30 at apositive output bias voltage (represented by reference number 84).Examples of the positive output bias voltage 84 include ≥1 kV, ≥2 kV,≥20 kV, or ≥60 kV.

Voltage multiplier 77 can be useful for bipolar devices such as bipolarx-ray tubes. The negative voltage multiplier 76, the positive voltagemultiplier 86, and the x-ray tube 31 can be oriented to minimizeelectrical field gradients. The x-ray tube 30 can be located in achannel 79 of the primary V-shape and in a channel 89 of the secondaryV-shape. Also, For example, as illustrated on x-ray sources 70 a and 80of FIGS. 7a , 8, and 9 the x-ray tube axis 31, extending from anelectron emitter associated with the cathode 91 to a target materialassociated with the anode 92, can be aligned with the channel 79 of theprimary V-shape and with the channel 89 of the secondary V-shape.Alternatively, as illustrated on x-ray source 70 b of FIG. 7b , thex-ray tube axis 31 can be misaligned with the channel 79 and the channel89. A choice between these designs can be made based on overall x-raysource enclosure limitations and required x-ray source voltage.

Another example of a design for minimizing electrical field gradients isx-ray source 80 in FIGS. 8-9 with a negative voltage multiplier 76, apositive voltage multiplier 86, and an x-ray tube 31 with structure asdescribed above, but oriented differently. Vectors will be used todescribe its orientation. A first vector V₁ can extend from a location(e.g. negative low voltage end 71 _(L)) on the negative low voltagesection 71 having a lowest absolute value of voltage to a location(negative high voltage end 72 _(H)) on the negative high voltage section72 having a highest absolute value of voltage. A second vector V₂ canextend from a location (e.g. positive low voltage end 81 _(L)) on thepositive low voltage section 81 having a lowest voltage to a location(positive high voltage end 82 _(H)) on the positive high voltage section82 having a highest voltage. An angle A₅ between the first vector V₁ andthe second vector V₂, viewed parallel to the x-ray tube axis 31, can be≥45°, ≥70°, ≥90°, or ≥110°; and can be ≤120°, ≤150°, or ≤170°.

Other examples of designs for minimizing electrical field gradients arex-ray sources 100 a and 100 b in FIGS. 10a-b , which are similar tothose described previously, but modified as follows. The first plane P₁and the third plane P₃ can be oriented to be parallel, as shown in FIG.10, or can be oriented to intersect with an angle of ≤3°, ≤5°, ≤10°,≤20°, or ≤30°. As another example, the second plane P₂ and the fourthplane P₄ can be parallel or can intersect with an angle A₆ of ≤150°,≤110°, ≤90°, ≤50°, ≤25°.

A negative voltage-sensing resistor 107 can be electrically coupledbetween the negative output bias voltage 74 and ground voltage 16, thenegative voltage-sensing resistor 107 located in a fifth plane P₅. Apositive voltage-sensing resistor 108 can be electrically coupledbetween the positive output bias voltage 84 and ground voltage 16, thepositive voltage-sensing resistor 108 located in a sixth plane P₆.

As shown in FIG. 10a , the negative low voltage section 71, the negativehigh voltage section 72, the positive low voltage section 81, thepositive high voltage section 82, the negative voltage-sensing resistor107, and the positive voltage-sensing resistor 108 can encircle thex-ray tube 30. As shown in FIGS. 10a-b , the first plane P₁, the secondplane P₂, the third plane P₃, the fourth plane P₄, the fifth plane P₅,and the sixth plane P₆ can encircle the x-ray tube 30.

Another example of minimizing electrical field gradients is to locatethe negative output bias voltage 74 and the positive output bias voltage84 on opposite sides of the x-ray tube 30. Located on opposite sides ofthe x-ray tube 30 means that a straight line 105, between the negativehigh voltage end 72h of the negative high voltage section 72 and thepositive high voltage end 82 _(H) of the positive high voltage section82, must pass through the x-ray tube 30.

X-Shape

Voltage multiplier 110, shown in FIGS. 11-16, includes a negativevoltage multiplier 111 and a positive voltage multiplier 112. Thenegative voltage multiplier 111 can multiply an input electrical voltageto produce a negative output bias voltage 74 having values of forexample ≤−500 volts, ≤−1 kV, ≤−2 kV, or ≤−10 kV. The negative voltagemultiplier 111 can have an end with a lowest absolute value of voltage,defining a negative low voltage end 111, and an end with a highestabsolute value of voltage, defining a negative high voltage end 111_(H). The positive voltage multiplier 112 can multiply an inputelectrical voltage to produce a positive output bias voltage 84 having avalue of for example ≥500 volts, ≥1 kV, ≥2 kV, or ≥10 kV. The positivevoltage multiplier 112 can have an end with a lowest voltage, defining apositive low voltage end 112 _(L), and an end with a highest voltage,defining a positive high voltage end 112 _(H). The negative voltagemultiplier 111 and the positive voltage multiplier 112 can be inclinedat different angles with respect to each other such that an end view ofthe voltage multipliers forms an X-shape by intersection of a planeP_(N) of the negative voltage multiplier 111 and a plane P_(P) of thepositive voltage multiplier 112.

Voltage multiplier 116 can be combined with an x-ray tube 30 to formx-ray sources 110 (FIGS. 11-12), 130 (FIG. 13), 140 (FIGS. 14), and 150(FIGS. 15a -16). The x-ray tube 30 can be located in a channel 119 ofthe X-shape. In order to reduce electrical field gradients, the negativevoltage multiplier 111 can be electrically coupled to a cathode 91 ofthe x-ray tube 30; can be located closer to the cathode 91 than thepositive voltage multiplier 112; and can provide electrical power to thecathode 91 at the negative output bias voltage 74. Also, the positivevoltage multiplier 112 can be electrically coupled to an anode 92 of thex-ray tube 30; can be located closer to the anode 92 than the negativevoltage multiplier 111; and can provide electrical power to the anode 92at the positive output bias voltage 84.

In order to reduce electrical field gradients, the x-ray tube axis 31,from an electron emitter associated with the cathode 91 to a targetmaterial associated with the anode 92, can be aligned with the channel119 of the X-shape. An angle of the channel 119 of the X-shape can be≥5°, ≥15 °, ≥30°, ≥45°, ≥60°, or ≥80° and can be ≤100°, ≤120°, ≤140°,≤160°, or ≤170°.

As shown in FIG. 11, to further smooth electrical field gradients and toreduce the chance of arcing failure, the x-ray tube 30 can be shiftedtowards the negative high voltage end 111 _(H) and/or towards thepositive high voltage end 112 _(H). For example, the negative lowvoltage end 111 _(L) can be ≥1.5 times farther, ≥2 times farther, ≥3times farther, or ≥4 times farther from the x-ray tube 30 than thenegative high voltage end 111 _(H). The positive low voltage end 112_(L) can be ≥1.5 times farther, ≥2 times farther, ≥3 times farther, or≥4 times farther from the x-ray tube 30 than the positive high voltageend 112 _(H).

In other words, D₃/D₄≥1.5, D₃/D₄≥2, D₃/D₄≥3, or D₃/D₄≥4; and/orD₅/D₆≥1.5, D₅/D₆≥2, D₅/D₆≥3, or D₅/D₆≥4; where D₃ is a distance betweenthe negative low voltage end 111 _(L) and the x-ray tube 30, D₄ is adistance between the negative high voltage end 111 _(H) and the x-raytube 30, D₅ is a distance between the positive low voltage end 112 _(L)and the x-ray tube 30, and D₆ is a distance between the positive highvoltage end 112 _(H) and the x-ray tube 30.

In one embodiment, the negative high voltage end 111 _(H) and/or thepositive high voltage end 112 _(H) can directly contact the x-ray tube30. The term “directly contact” of the prior sentence means that theelectronic component(s) of the negative high voltage end 111 _(H) and/orthe positive high voltage end 112 _(H) touch the x-ray tube 30, notmerely that a wire electrically connects the negative high voltage end111H and/or the positive high voltage end 112 _(H) to the x-ray tube 30.Thus, D₃/D₄ can equal infinity if D₄=0 and D₅/D₆ can equal infinity ifD₆=0.

As shown in FIG. 13, in order to reduce electrical field gradients, thelow voltage ends 111 _(L) and 112 _(L) can be closer to each other thanthe high voltage ends 111 _(H) and 112 _(H) are to each other. Thus, forexample a distance D_(H) between the positive high voltage end 112 _(H)and the negative high voltage end 111 _(H) can be ≥2 times, ≥3 times, ≥4times, or ≥5 times a distance D_(L) between the positive low voltage end112 _(L) and the negative low voltage end 111 _(L)

As shown in FIGS. 13-15 b, the negative voltage multiplier 111 and thepositive voltage multiplier 112 can intersect in the end view. As shownin FIG. 14, a length L₁ or L₂ of each leg of the negative voltagemultiplier 111 in the X-shape can be ≥5%, ≥10%, ≥10%, or ≥20% of a totallength (L₁+L₂) of the negative voltage multiplier 111. A length L₃ or L₄each leg of the positive voltage multiplier 112 in the X-shape can be≥5%, ≥10%, ≥10%, or ≥20% of a total length (L₃+L₄) of the positivevoltage multiplier 112.

As shown in FIGS. 15a -16, a corona guard 35 can have a curved profile.The curved profile can wrap at least partially around the negativevoltage multiplier 111, the positive voltage multiplier 112, and/or acurved, cylindrical shape of the x-ray tube 30. Thus for example, thecurved profile can wrap ≥135°, ≥180°, ≥270°, or ≥315° of a 360°circumference around the negative voltage multiplier 111, the positivevoltage multiplier 112, and/or the curved, cylindrical shape of the xraytube 30. For example, the curved profile of FIGS. 15a and 15b wrapsabout 290° of the 360° circumference. The curved profile of the coronaguard 35 is shown in FIGS. 15a -16 with a consistent cross-sectionalshape along x-ray tube axis 31. The curved profile, however, can have anarrowing shape profile or shape (similar to a conical shape) for spacesaving and improved electrical field gradients. For example, the curvedprofile of the corona guard 35 can be closer to the x-ray tube 30 or thevoltage multiplier 10 near lower voltages and farther away near highervoltages.

The corona guard 35 can have a material at a concave side of the curvedprofile with an electrical resistivity of ≥10⁵ Ω*m, ≥10⁷ Ω*m, or ≥10 ¹¹Ω*m. This material can be or can include ceramic. A material at a convexside of the curved profile can have a lower electrical resistivity thanthe material at the concave side. This provides anelectrically-insulative surface facing the voltage multiplier to reducethe chance of arcing and a surface with relatively higher electricalconductivity at the convex side for shaping and smoothing electricalfield gradients. Thus, for example, an electrical resistivity of thematerial at the concave side of the curved profile divided by anelectrical resistivity of the material at the convex side of the curvedprofile can be ≥10⁴, ≥10⁶, ≥10⁸, ≥10¹⁰, ≥10¹², or ≥10¹⁴.

One option for the material at a convex side is a negative voltagesensor 159 electrically coupled to the negative output bias voltage 74and/or a positive voltage sensor 169 electrically coupled to thepositive output bias voltage 84. This provides the dual benefit ofproviding a material with a lower electrical resistivity than thematerial at the concave side and saves space. Voltage-sensing resistorstake valuable space, especially in portable x-ray sources, and savingthis space can be a substantial benefit. Another problem with standardvoltage-sensing resistors is that they typically have a rectangularshape, with corners where electrical field gradients can be high, thusincreasing the chance of arcing failure. Putting such voltage-sensingresistors 159 and 169 on the smooth curved profile can help avoid sucharcing failure.

The voltage-sensing resistors 159 and 169 can be a dielectric inkpainted on the convex side. The voltage-sensing resistors 159 and 169can wrap around a substantial portion of the voltage multiplier 116and/or the curved, cylindrical shape of the x-ray tube 30, such as forexample ≥135°, ≥180°, ≥270°, or ≥315° of the 360° circumference of thevoltage multiplier 10 and/or the curved, cylindrical shape of the x-raytube 30. For example, the curved profile of the voltage-sensingresistors 159 and 169 of FIGS. 15a and 15b wraps about 290° of the 360°circumference,

Curved Shape

As shown in FIGS. 17a-17b , voltage multipliers 171 and 172 can includea first end 171 _(L) having a lowest absolute value of voltage and asecond end 171 _(H) having a highest absolute value of voltage. Therecan be a gradually increasing absolute value of voltage from the firstend 171 _(L) to the second end 171 _(H). The voltage multiplier 171 or172 can multiply an input electrical voltage to produce an output biasvoltage, having an absolute value of or example ≥1 kV, ≥2 kV, ≥10 kV, or≥30 kV, between the first end 171 _(L) and the second end 171 _(H).

The voltage multipliers 171 and 172 can include a curved shape. Adirection 171 _(C) of the increasing absolute value of voltage can wrapin the curved shape at least partially around an axis, defining avoltage multiplier axis 173. Thus for example, the curved shape can wrap≥45°, ≥90°, ≥135°, ≥180°, ≥270°, or ≥315° of a 360° circumference aroundthe voltage multiplier axis 173. For example, the curved shapes of FIGS.17a and 17b wrap about 150° of the 360° circumference.

The curved profile of the corona guard 35 and the curved shape of thevoltage multipliers 171, 172, 181, and 182 in FIGS. 17a -22 are shownwith a consistent cross-sectional shape along the voltage multiplieraxis 173 and the x-ray tube axis 31. The curved profile and the curvedshape, however, can have a narrowing profile or shape (similar to aconical shape) for space saving and improved electrical field gradients.For example, the curved profile of the corona guard 35, the curved shapeof the voltage multipliers 171, 172, 181, or both can be closer to thex-ray tube 30 near lower voltages and farther away near higher voltages.

The curved shape can form a “C” shape. The curved shape can becontinuous and smooth, such as with a flexible circuit board, as shownin FIG. 17a . Alternatively, the curved shape can be formed by multiplesmall sections 174 hinged to form the curved shape, as shown in FIG. 17b. For example, a hinged, curved shape, like that of FIG. 17b can include≥4 sections 174, ≥6 sections 174, ≥8 sections 174, ≥10 sections 174, or≥20 sections 174. In one embodiment, every junction or hinge betweeneach pair of adjacent sections 174 can bend the sections 174 inwardtowards the voltage multiplier axis 173, as shown in FIG. 17 b.

An x-ray tube 30 can be located on a concave side of the curved shape.The output bias voltage can be electrically coupled to the x-ray tube30. The voltage multiplier axis 173 can be aligned with the x-ray tubeaxis 31.

The voltage multiplier 180 of FIGS. 18-22 is similar to voltagemultipliers 171 and 172, except that voltage multiplier 180 includesboth a negative voltage multiplier 181 and a positive voltage multiplier182. The negative voltage multiplier 181 can multiply an inputelectrical voltage from a first end 181 _(L) having a lowest absolutevalue of voltage, to a second end 181 _(H) having a highest absolutevalue of voltage, with a gradually increasing absolute value of voltagefrom the first terminal 181 _(L) to the second terminal 181 _(H), toprovide ≤−1 kV, ≤−2 kV, ≤−10 kV, or −30 kV of negative output biasvoltage 74.

The negative voltage multiplier 181 can include a primary curved shapewith a direction 181 _(C) of the increasing absolute value of voltagewrapping in the primary curved shape at least partially around thevoltage multiplier axis 173. Thus for example, the primary curved shapecan wrap ≥45°, ≥90°, ≥135°, ≥180°, ≥270°, or ≥315° of a 360°circumference around the voltage multiplier axis 173.

The positive voltage multiplier 182 can multiply an input electricalvoltage from a first terminal 182 _(L) having a lowest voltage, to asecond terminal 182 _(H) having a highest voltage, with a graduallyincreasing voltage from the first terminal 182 _(L) to the secondterminal 182 _(H), to provide ≥1 kV, ≥2 kV, ≥10 kV, or ≥30 kV ofpositive output bias voltage 84.

The positive voltage multiplier 182 can include a secondary curved shapewith a direction 182 _(C) of the increasing voltage wrapping in thesecondary curved shape at least partially around the voltage multiplieraxis 173. Thus for example, the secondary curved shape can wrap ≥45°,≥90°, ≥135°, ≥180°, ≥270°, or ≥315° of a 360° circumference around thevoltage multiplier axis 173.

As shown in FIGS. 19-22, x-ray sources 190, 210, and 220 can comprise anx-ray tube 30 and voltage multiplier 180. The x-ray tube 30 can belocated on a concave side of the primary curved shape and/or on aconcave side of the secondary curved shape. The negative voltagemultiplier 181 can be electrically coupled to and can provide electricalpower at the negative output bias voltage 74 to a cathode 91 of thex-ray tube 30. The positive voltage multiplier 182 can be electricallycoupled to and can provide electrical power at the positive output biasvoltage 84 to an anode 92. of the x-ray tube 30. The voltage multiplieraxis 173 can be aligned with the x-ray tube axis 31, the x-ray tube axis31 extending from an electron emitter associated with the cathode 91 toa target material associated with the anode 92.

A shown in FIG. 21, the first end 181 _(L) can be ≥1.5 times farther, ≥2times farther, ≥3 times farther, or ≥4 times farther than the second end181 _(H) from the x-ray tube 30. The first terminal 182 _(L) can be ≥1.5times farther, ≥2 times farther, ≥3 times farther, or ≥4 times fartherthan the second terminal 182 _(H) from the x-ray tube 30. This designcan reduce electrical field gradients and can reduce the risk of arcingfailure.

A shown in FIGS. 21-22, a corona guard 35 can include a curved profile.The curved profile can be aligned with the x-ray tube axis 31 and/or thevoltage multiplier axis 173. The curved profile can wrap at leastpartially around the voltage multiplier 180 and/or a curved, cylindricalshape of the x-ray tube 30. Thus for example, the curved profile canwrap ≥135°, ≥180°, ≥270°, or ≥315° of a 360° circumference around thevoltage multiplier 180 and/or a curved, cylindrical shape of the x-raytube 30.

The corona guard 35 can have a material at a concave side of the curvedprofile with a high electrical resistivity and/or a material at a convexside of the curved profile with a lower electrical resistivity asdescribed above. One option for the material at a convex side is anegative voltage sensor 206 electrically coupled to the negative outputbias voltage 74 and/or a positive voltage sensor 207 electricallycoupled to the positive output bias voltage 84. This provides benefitsas described above with voltage-sensing resistors 159 and 169.

For improved shaping of electrical fields, a direction 206 _(C) ofincreasing absolute value of voltage in the negative voltage sensor 181can align with the direction 181 _(C) of increasing absolute value ofvoltage in the primary curved shape, and/or a direction 207 _(C) ofincreasing voltage in the positive voltage sensor 182 can align with thedirection 182 _(C) of increasing voltage in the secondary curved shape.

The voltage-sensing resistors 206 and 207 can be a dielectric inkpainted on the convex side. The voltage-sensing resistors 206 and 207can wrap around a substantial portion of the voltage multiplier 180and/or the curved, cylindrical shape of the x-ray tube 30, such as forexample ≥135°, ≥180°, ≥270°, or ≥315° of a 360° circumference.

For improved shaping of electrical field gradients, as shown in FIGS.21-22, the second end 181 _(H) of the negative voltage multiplier 181and the second terminal 182 _(H) of the positive voltage multiplier 182can be located on opposite sides of the x-ray tube 30. Also, the primarycurved shape or the secondary curved shape can wrap clockwise around thevoltage multiplier axis 173 as viewed from an end of the voltagemultiplier axis 173 and the other of the primary curved shape or thesecondary curved shape can wrap counterclockwise around the voltagemultiplier axis 173.

Reliability of the voltage multipliers described herein can be improvedwhile also minimizing size and cost, by using different sized electroniccomponents 13, such as capacitors and/or diodes, at different locationson the voltage multiplier. Larger electronic components 13 (e.g.capacitors/diodes with a higher voltage rating) can be used at or closerto a lowest voltage end and smaller electronic components 13 (e.g.capacitors/diodes with a lower voltage rating) can be used at or closerto a highest voltage end. Thus, the figures show two or three differentsized electronic components 13 which can be capacitors or diodes. Forexample, for voltage multipliers in FIGS. 1-10, the low voltage section11 can include capacitors and/or diodes with a voltage rating that is≥10% higher than capacitors and/or diodes of the high voltage section12. As another example, for voltage multipliers in FIGS. 11-14, thenegative low voltage end 111 _(L) can include capacitors and/or diodeswith a voltage rating that is ≥10% higher than capacitors and/or diodesat the negative high voltage end 111 _(H); and the positive low voltageend 112 _(L) can include capacitors and/or diodes with a voltage ratingthat is ≥10% higher than capacitors and/or diodes at the positive highvoltage end 112 _(H). As another example, for voltage multipliers inFIGS. 15-22, the voltage multiplier can include capacitors and/or diodesclosest to the first end 171 _(L) with a voltage rating that is ≥10%higher than capacitors and/or diodes closest to the second end 171 _(H).

The voltage multipliers described herein can be any voltagemultiplier/generator capable of receiving an input voltage andmultiplying that voltage to generate ≥1 kV of output voltage. Forexample, the voltage multipliers described herein can be aCockcroft-Walton multipliers/generators; the voltage multipliersdescribed herein can be half wave or full wave. The electroniccomponents in the figures are shown on a side of the circuit boardfacing the channel 19, 79, and 89 of the V-shape, the x-ray tube axis31, the channel 119 of the X-shape, and the voltage multiplier axis 173,but these electronic components can be located on an opposite side ofthe circuit board or on both sides of the circuit board.

What is claimed is:
 1. A voltage multiplier configured to multiply aninput electrical voltage to produce an output bias voltage having anabsolute value of ≥2 kV, the voltage multiplier comprising: a lowvoltage section located in a first plane and a high voltage sectionlocated in a second plane; the first plane and the second plane forminga V-shape with an angle of a channel of the V-shape being ≥60° and≤170°; the low voltage section configured to produce ≥1 kV absolutevalue of bias voltage and providing input electrical power to the highvoltage section; and the high voltage section configured to produce ≥1kV absolute value of bias voltage and providing output electrical powerto a high voltage apparatus at the output bias voltage.
 2. The voltagemultiplier of claim 1, further comprising: a corona guard including acurved profile, the curved profile wrapping at least partially aroundthe voltage multiplier; and an electrical resistivity of a material at aconcave side of the curved profile divided by an electrical resistivityof a material at a convex side of the curved profile being ≥10⁶.
 3. Thevoltage multiplier of claim 1, further comprising: a middle voltagesection electrically coupled between the low voltage section and thehigh voltage section; the middle voltage section configured to produce≥1 kV absolute value of bias voltage and providing input electricalpower to the high voltage section; the middle voltage section located ina seventh plane, the seventh plane being different from the first planeand the second piane; and an angle between the seventh plane and thefirst plane and an angle between the seventh plane and the second plane,both located on a same side of the seventh plane, both have a value of≥70° and ≤170°.
 4. The voltage multiplier of claim 1, furthercomprising: the V-shape is a primary V-shape, the voltage multiplier isa negative voltage multiplier, the output bias voltage is a negativeoutput bias voltage, the low voltage section is a negative low voltagesection, and the high voltage section is a negative high voltagesection; a positive voltage multiplier configured to multiply an inputelectrical voltage to produce a positive output bias voltage of ≥2 kV,the positive voltage multiplier comprising: a positive low voltagesection located in a third plane and a positive high voltage sectionlocated in a fourth plane; the third plane and the fourth plane forminga secondary V-shape with an angle of an opening of the secondary V-shapebeing ≥60° and ≤170°; the positive low voltage section configured toproduce ≥1 kV of bias voltage and providing input electrical power to aninput of the positive high voltage section; and the positive highvoltage section configured to produce ≥1 kV of bias voltage andconfigured to provide the positive output bias voltage.
 5. The voltagemultiplier of claim 4, wherein the first plane and the third plane areparallel or intersect with an angle of ≤10°.
 6. The voltage multiplierof claim 4, further comprising: a negative voltage sensing resistorelectrically coupled between the negative output bias voltage and groundvoltage, the negative voltage sensing resistor located in a fifth plane;and a positive voltage sensing resistor electrically coupled between thepositive output bias voltage and ground voltage, the positive voltagesensing resistor located in a sixth plane.
 7. The voltage multiplier ofclaim 4, wherein the second plane and the fourth plane are parallel orintersect with an angle of ≤90°.
 8. A voltage multiplier comprising: anegative voltage multiplier configured to multiply an input electricalvoltage to produce a negative output bias voltage having a value of ≤−2kV, the negative voltage multiplier having an end with a lowest absolutevalue of voltage, defining a negative low voltage end, and an end with ahighest absolute value of voltage, defining a negative high voltage end;a positive voltage multiplier configured to multiply an input electricalvoltage to produce a positive output bias voltage having a value of ≤2kV, the positive voltage multiplier having an end with a lowest voltage,defining a positive low voltage end, and an end with a highest voltage,defining a positive high voltage end; and the negative voltagemultiplier and the positive voltage multiplier inclined at differentangles with respect to each other such that an end view of the voltagemultipliers forms an X-shape by intersection of a plane of the negativevoltage multiplier and a plane of the positive voltage multiplier. 9.The voltage multiplier of claim 8, wherein: the negative low voltage endincludes capacitors with a voltage rating that is ≥10% higher thancapacitors at the negative high voltage end; the negative low voltageend includes diodes with a voltage rating that is ≥10% higher thandiodes at the negative high voltage end; the positive low voltage endincludes diodes with a voltage rating that is ≥10% higher than diodes atthe positive high voltage end; and the positive low voltage end includescapacitors with a voltage rating that is ≥10% higher than capacitors atthe positive high voltage end.
 10. The voltage multiplier of claim 8,wherein a distance between the positive high voltage end and thenegative high voltage end is ≥3 times a distance between the positivelow voltage end and the negative low voltage end.
 11. The voltagemultiplier of claim 8, wherein the voltage multipliers intersect in theend view with: a length each leg of the negative voltage multiplier inthe X-shape being ≥10% of a total length of the negative voltagemultiplier; and a length each leg of the positive voltage multiplier inthe X-shape being ≥10% of a total length of the positive voltagemultiplier on each side of the X-shape.
 12. The voltage multiplier ofclaim 8, wherein an angle of a channel of the X-shape is ≥60° and ≤120°.13. The voltage multiplier of claim 8, further comprising: a coronaguard including a curved profile, the curved profile wrapping ≥partiallyaround the negative voltage multiplier and the positive voltagemultiplier; and an electrical resistivity of a material at a concaveside of the curved profile divided by an electrical resistivity of amaterial at a convex side of the curved profile being ≥10 ⁶.
 14. Thevoltage multiplier of claim 8, further comprising: a corona guard; thecorona guard including a curved profile wrapping at least partiallyaround the negative voltage multiplier and the positive voltagemultiplier; the corona guard having a material at a concave side of thecurved profile with an electrical resistivity of ≥10⁵ Ω*rn; and avoltage sensor electrically coupled to the output bias voltage andlocated on a convex side of the curved profile. a negative voltagesensor electrically coupled to the negative output bias voltage andlocated on a convex side of the curved profile; and a positive voltagesensor electrically coupled to the positive output bias voltage andlocated on the convex side of the curved profile.
 15. A voltagemultiplier configured to multiply an input electrical voltage to producean output bias voltage having an absolute value of ≥2 kV, the voltagemultiplier comprising: a first end having a lowest absolute value ofvoltage and a second end having a highest absolute value of voltage, agradually increasing absolute value of voltage from the first end to thesecond end, the voltage multiplier configured to produce ≥2 kV ofabsolute value bias voltage between the first end and the second end;and a curved shape with a direction of the increasing absolute value ofvoltage wrapping in the curved shape at least partially around an axis,defining a voltage multiplier axis.
 16. The voltage multiplier of claim15, further comprising: a corona guard including a curved profile, thecurved profile wrapping at least partially around the voltagemultiplier; and an electrical resistivity of a material at a concaveside of the curved profile divided by an electrical resistivity of amaterial at a convex side of the curved profile being ≥10⁶.
 17. Thevoltage multiplier of claim 15, further comprising: a corona guard; thecorona guard including a curved profile wrapping at least partiallyaround the voltage multiplier; the corona guard having a material at aconcave side of the curved profile with an electrical resistivity of≥10⁵ Ω*m; and a voltage sensor electrically coupled to the output biasvoltage and located on a convex side of the curved profile.
 18. Thevoltage multiplier of claim 15, further comprising: the voltagemultiplier is a negative voltage multiplier, the output bias voltage isa negative output bias voltage of ≤−2 kV, and the curved shape is aprimary curved shape; a positive voltage multiplier, the positivevoltage multiplier: configured to multiply an input electrical voltagefrom a first terminal having a lowest voltage, to a second terminalhaving a highest voltage, with a gradually increasing voltage from thefirst terminal to the second terminal, to provide ≥2 kV of positiveoutput bias voltage; and including a secondary curved shape with adirection of the increasing voltage wrapping in the secondary curvedshape at least partially around the voltage multiplier axis.
 19. Thevoltage multiplier of claim 15, wherein the primary curved shape or thesecondary curved shape wraps clockwise around the voltage multiplieraxis as viewed from an end of the voltage multiplier axis and the otherof the primary curved shape or the secondary curved shape wrapscounterclockwise around the voltage multiplier axis.
 20. The voltagemultiplier of claim 15, further comprising: a corona guard; the coronaguard including a curved profile wrapping at least partially around thenegative voltage multiplier and the positive voltage multiplier; thecorona guard having a material at a concave side of the curved profilewith an electrical resistivity of ≥10⁵ Ω*m; a negative voltage sensorelectrically coupled to the negative output bias voltage and located ona convex side of the curved profile; a positive voltage sensorelectrically coupled to the positive output bias voltage and located ona convex side of the curved profile; a direction of increasing absolutevalue of voltage in the negative voltage sensor aligns with thedirection of the increasing absolute value of voltage in the primarycurved shape; and a direction of increasing voltage in the positivevoltage sensor aligns with the direction of the increasing voltage inthe secondary curved shape.